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int(-pi//4)^(pi//4) \ (e^x sec^2 \ dx)/(...

`int_(-pi//4)^(pi//4) \ (e^x sec^2 \ dx)/(e^(2x)-1)` is equal to (i)`0` (ii)`2` (iii)`e` (iv)none of these

A

0

B

2

C

e

D

2e

Text Solution

Verified by Experts

The correct Answer is:
A
Let `int_(-(pi)/(4))^((pi)/(4))(e^(x)sec^(2)xdx)/(e^(2x)-1)`
If `f(x)=(e^(x)sec^(2)x)/(e^(2x)-1)`
`therefore" "f(-x)=(e^(-x)sec^(2)x)/(e^(-2x)_1)`
`=(e^(x)sec^(2)x)/(1-e^(2x))`
`=(e^(x)sec^(2)x)/(e^(2x)-1)`
`=-f(x)`
`therefore` f(x) is an odd functions.
`therefore" I=0`
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